5L 7s: Difference between revisions

(13 intermediate revisions by 10 users not shown)

Line 1:

{{interwiki

| de =

| en = 5L 7s

| es =

| ja = 5L 7s

}}

5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[~~Schismatic family|~~schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing ~~superpyth~~[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]].

5L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing Superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]].

The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean tuning or the schismatic temperament, and on the other hand, the simpler and less accurate temperament known as superpyth in which 64/63 is tempered out.

== Scale properties ==

=== Intervals ===

=== Generator chain ===

=== Modes ===

The ~~two distinct harmonic entropy minima~~ are~~, on~~ the ~~one hand, scales very close~~ to ~~Pythagorean such that~~ [[~~64/63~~]] ~~is not tempered out~~, ~~such as the schismatic temperaments known as Helmholtz and Garibaldi~~, ~~and on the other hand~~, ~~the much simpler and less accurate~~ scale ~~known as superpyth~~ in ~~which 64/63 is tempered out~~.

=== Proposed names ===

The modes are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China.

~~== Modes ==~~

{{MOS modes

~~The~~ modes ~~are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature.~~

| Mode Names=

* 11|~~0 LsLsLssLsLss -~~ Rat

Rat $

* 10|1 LsLssLsLsLss - Ox

Ox $

* 9|2 LsLssLsLssLs - Tiger

Tiger $

* 8|3 LssLsLsLssLs - Rabbit

Rabbit $

* 7|4 LssLsLssLsLs - Dragon

Dragon $

* 6|5 sLsLsLssLsLs - Snake

Snake $

* 5|6 sLsLssLsLsLs - Horse

Horse $

* 4|7 sLsLssLsLssL - Goat

Goat $

* 3|8 sLssLsLsLssL - Monkey

Monkey $

* 2|9 sLssLsLssLsL - Rooster

Rooster $

* 1|10 ssLsLsLssLsL - Dog

Dog $

* 0|11 ssLsLssLsLsL - Pig

Pig $

}}

== Scales ==

Line 27:

Line 49:

* [[Pepperoni12]] – 271edo tuning

* [[Supra12]] – 56edo tuning

* [[Archy12]] – ~~472edo~~ tuning

* [[Archy12]] – 49edo tuning

* [[12-22a]] – 22edo tuning

== Scale tree ==

{{~~Scale tree~~|~~Comments=~~6/5: [[Photia]] ~~/ [[pontiac]] /~~ [[grackle]];

{{MOS tuning spectrum

5/4: [[Helmholtz]], [[Pythagorean tuning]] (701.~~9550¢~~);

| 6/5 = [[Photia]], ↑ [[grackle]]

9/7: [[Garibaldi]] / [[cassandra]];

| 5/4 = [[Helmholtz (temperament)|Helmholtz]], [[Pythagorean tuning]] (701.955{{c}})

4/3: Garibaldi / [[andromeda]];

| 9/7 = [[Garibaldi]] / [[cassandra]]

11/8: [[Kwai]];

| 4/3 = Garibaldi / [[andromeda]]

10/7: [[Undecental]];

| 11/8 = [[Kwai]]

3/2: [[Edson]];

| 10/7 = [[Undecental]], argent tuning (702.944{{c}})

13/8~~: Golden~~ neogothic (704.~~0956¢~~);

| 3/2 = [[Edson]]

5/3: [[Leapday]] / [[~~polypyth~~]];

| 13/8 = [[Polypyth]], golden neogothic (704.096{{c}})

12/7: [[~~Leapweek~~]];

| 5/3 = [[Leapday]]

7/3: [[Supra]];

| 12/7 = [[Leapweek]]

13/5: Golden supra (708.~~0539¢~~);

| 9/5 = [[Leapmonth]]

8/3: [[Quasisuper]] / [[quasisupra]];

| 7/3 = [[Supra]]

3/1: [[Suprapyth]];

| 13/5 = Golden supra (708.054{{c}})

7/2: [[Superpyth]];

| 8/3 = [[Quasisuper]] / [[quasisupra]]

6/1: ↓ [[~~Ultrapyth~~]] / [[~~Oceanfront scales|Oceanfront~~]]

| 3/1 = [[Suprapyth]]

| 7/2 = [[Superpyth]]

| 6/1 = ↓ [[Oceanfront]] / [[ultrapyth]]

}}

[[Category:12-tone scales]]

[[Category:P-chromatic| ]]

[[Category:Chromatic scales]]

@@ Line 1: / Line 1: @@
+{{interwiki
+| de =
+| en = 5L 7s
+| es =
+| ja = 5L 7s
+}}
 {{Infobox MOS}}
 {{MOS intro|Other Names=p-chromatic}}
-L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[Schismatic family|schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]].
+L 7s represents the chromatic scales of [[Pythagorean tuning|Pythagorean]]/[[schismic]] and [[superpyth]], the former being [[Rothenberg propriety|proper]] but the latter improper until expanded by 5 more notes, producing Superpyth[17]. Such scales are characterized by having a small step ([[diatonic semitone]]) that is smaller than the [[chroma]] ([[chromatic semitone]]), the reverse of [[7L 5s]].
+The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean tuning or the schismatic temperament, and on the other hand, the simpler and less accurate temperament known as superpyth in which 64/63 is tempered out.
+== Scale properties ==
+{{TAMNAMS use}}
+=== Intervals ===
+{{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
+{{MOS mode degrees}}
-The two distinct harmonic entropy minima are, on the one hand, scales very close to Pythagorean such that [[64/63]] is not tempered out, such as the schismatic temperaments known as Helmholtz and Garibaldi, and on the other hand, the much simpler and less accurate scale known as superpyth in which 64/63 is tempered out.
+=== Proposed names ===
+The modes are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature. Furthermore, 12edo (equalized tuning of this MOS) was independently discovered in China.
-== Modes ==
+{{MOS modes
-The modes are named by [[Eliora]] after Chinese zodiac animals. 5L 7s is the opposite mos to [[7L 5s]], named after a Western concept, Gregorian months, therefore this mos scale has Eastern nomenclature.
+| Mode Names=
-* 11|0 LsLsLssLsLss - Rat
+Rat $
-* 10|1 LsLssLsLsLss - Ox
+Ox $
-* 9|2 LsLssLsLssLs - Tiger
+Tiger $
-* 8|3 LssLsLsLssLs - Rabbit
+Rabbit $
-* 7|4 LssLsLssLsLs - Dragon
+Dragon $
-* 6|5 sLsLsLssLsLs - Snake
+Snake $
-* 5|6 sLsLssLsLsLs - Horse
+Horse $
-* 4|7 sLsLssLsLssL - Goat
+Goat $
-* 3|8 sLssLsLsLssL - Monkey
+Monkey $
-* 2|9 sLssLsLssLsL - Rooster
+Rooster $
-* 1|10 ssLsLsLssLsL - Dog
+Dog $
-* 0|11 ssLsLssLsLsL - Pig
+Pig $
+}}
 == Scales ==
@@ Line 27: / Line 49: @@
 * [[Pepperoni12]] – 271edo tuning
 * [[Supra12]] – 56edo tuning
-* [[Archy12]] – 472edo tuning
+* [[Archy12]] – 49edo tuning
 * [[12-22a]] – 22edo tuning
 == Scale tree ==
-{{Scale tree|Comments=6/5: [[Photia]] / [[pontiac]] / [[grackle]];
+{{MOS tuning spectrum
-/4: [[Helmholtz]], [[Pythagorean tuning]] (701.9550¢);
+| 6/5 = [[Photia]], ↑&nbsp;[[grackle]]
-/7: [[Garibaldi]] / [[cassandra]];
+| 5/4 = [[Helmholtz (temperament)|Helmholtz]], [[Pythagorean tuning]] (701.955{{c}})
-/3: Garibaldi / [[andromeda]];
+| 9/7 = [[Garibaldi]] / [[cassandra]]
-/8: [[Kwai]];
+| 4/3 = Garibaldi / [[andromeda]]
-/7: [[Undecental]];
+| 11/8 = [[Kwai]]
-/2: [[Edson]];
+| 10/7 = [[Undecental]], argent tuning (702.944{{c}})
-/8: Golden neogothic (704.0956¢);
+| 3/2 = [[Edson]]
-/3: [[Leapday]] / [[polypyth]];
+| 13/8 = [[Polypyth]], golden neogothic (704.096{{c}})
-/7: [[Leapweek]];
+| 5/3 = [[Leapday]]
-/3: [[Supra]];
+| 12/7 = [[Leapweek]]
-/5: Golden supra (708.0539¢);
+| 9/5 = [[Leapmonth]]
-/3: [[Quasisuper]] / [[quasisupra]];
+| 7/3 = [[Supra]]
-/1: [[Suprapyth]];
+| 13/5 = Golden supra (708.054{{c}})
-/2: [[Superpyth]];
+| 8/3 = [[Quasisuper]] / [[quasisupra]]
-/1: ↓ [[Ultrapyth]] / [[Oceanfront scales|Oceanfront]]
+| 3/1 = [[Suprapyth]]
+| 7/2 = [[Superpyth]]
+| 6/1 = ↓&nbsp;[[Oceanfront]] / [[ultrapyth]]
 }}
 [[Category:12-tone scales]]
 [[Category:P-chromatic| ]]<!-- main article -->
 [[Category:Chromatic scales]]